\documentclass[a4paper,11pt]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[french]{babel}
\usepackage[a4paper,top=3.2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{fancyhdr}
\usepackage{qrcode}
\usepackage[table]{xcolor}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
% Puces nettes (babel-french remplace sinon la puce par un tiret « – » peu pro).
% Vaut pour TOUTES les fiches qui importent ce module. AtBeginDocument pour
% passer après la personnalisation des listes faite par babel-french.
\AtBeginDocument{%
  \setlist[itemize]{leftmargin=1.8em,itemsep=0.5ex,topsep=0.4ex,parsep=0pt}%
  \setlist[itemize,1]{label=\textcolor{red!75!black}{\small\textbullet}}%
  \setlist[itemize,2]{label=\textcolor{red!75!black}{\scriptsize\textbullet}}%
}
% Titres compacts (gain de place vertical, fiches plus denses) — vaut pour tous.
\usepackage{titlesec}
\titlespacing*{\section}{0pt}{1.4ex}{0.6ex}
\titlespacing*{\subsection}{0pt}{1.0ex}{0.3ex}
% multicol : listes denses (calcul mental) sur 2 colonnes — neutre tant qu'il
% n'est pas utilisé, dispo pour tous les générateurs.
\usepackage{multicol}
\setlength{\columnsep}{1.5em}
% needspace : empêche un titre d'exercice de rester orphelin en bas de page
% (réserve quelques lignes ; sinon le titre passe à la page suivante avec sa
% liste). Neutre tant qu'il n'est pas appelé — dispo pour tous les générateurs.
\usepackage{needspace}
\usepackage{tikz}
\usetikzlibrary{decorations.text}

\usepackage{tgheros}
\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{75pt}
\setlength{\headsep}{10pt}

\newcommand{\logowouf}{%
\begin{tikzpicture}[baseline={(current bounding box.center)},scale=0.55,
                    line cap=round,line join=round]
    \path[use as bounding box] (-2.20,-1.45) rectangle (2.20,2.20);
    \path[
        postaction={decorate},
        decoration={
            text along path,
            text={|\fontfamily{qhv}\bfseries\fontsize{9}{9}\selectfont|site2wouf.fr},
            text align={center},
            raise=0.03ex
        }
    ] (-1.29,0.48) arc[start angle=160,end angle=20,radius=1.29];
    \begin{scope}[xshift=-0.06cm]
        \fill[black] (-0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] ( 0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] (-0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black] ( 0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black]
            (0,-0.10)
            .. controls (-0.36,-0.02) and (-0.63,-0.24) .. (-0.58,-0.58)
            .. controls (-0.52,-0.93) and (-0.16,-1.12) .. (0,-0.90)
            .. controls (0.16,-1.12) and (0.52,-0.93) .. (0.58,-0.58)
            .. controls (0.63,-0.24) and (0.36,-0.02) .. (0,-0.10)
            -- cycle;
    \end{scope}
\end{tikzpicture}%
}

\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 343}

\fancyhead[C]{%
\raisebox{4pt}{%
\begin{minipage}[c]{0.15\textwidth}
    \centering
    \logowouf
\end{minipage}
\begin{minipage}[c]{0.62\textwidth}
    \centering
    {\Large\bfseries \titre\par}
    {\small\color{gray} \soustitre}
\end{minipage}
\begin{minipage}[c]{0.21\textwidth}
    \centering
    \qrcode[height=1.5cm]{https://site2wouf.fr/exercices_conversions_cycle3.php?x=343}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0343}
\end{minipage}%
}
}

\begin{document}

\begin{center}
    \small Fractions décimales, multiplication/division par 10, 100, 1 000, conversions d'unités.
\end{center}
\vspace{0.5em}
\sloppy

\needspace{5\baselineskip}
\section*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{84}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{22}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ 100
\item   430  ~ \(\times\)  ~ 100
\item   31,9  ~ \(\times\)  ~ 10
\item   72,7  ~ \(\times\)  ~ 10
\item   353  ~ \(\times\)  ~ 100
\item   0,03  ~ \(\times\)  ~ 100
\item   0,05  ~ \(\times\)  ~ 100
\item   0,831  ~ \(\times\)  ~ 1 000
\item   4,71  ~ \(\times\)  ~ 1 000
\item   562  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   796,4  ~ : ~ 100
\item   7 610  ~ : ~ 10
\item   22,15  ~ : ~ 10
\item   1 298  ~ : ~ 1 000
\item   63,45  ~ : ~ 10
\item   1 528  ~ : ~ 100
\item   3 345  ~ : ~ 10
\item   9 649  ~ : ~ 10
\item   555,1  ~ : ~ 1 000
\item   94,97  ~ : ~ 10
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   79  ~ \(\times\)  ~ ... ~ = ~ 7 900
\item   0,52  ~ \(\times\)  ~ ... ~ = ~ 520
\item   4,75  ~ \(\times\)  ~ ... ~ = ~ 475
\item   58,9  ~ \(\times\)  ~ ... ~ = ~ 58 900
\item   0,085  ~ \(\times\)  ~ ... ~ = ~ 8,5
\item   9,68  ~ \(\times\)  ~ ... ~ = ~ 96,8
\item   0,65  ~ \(\times\)  ~ ... ~ = ~ 6,5
\item   73,5  ~ \(\times\)  ~ ... ~ = ~ 735
\item   0,054  ~ \(\times\)  ~ ... ~ = ~ 5,4
\item   0,009  ~ \(\times\)  ~ ... ~ = ~ 9
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   5 436  ~ \(\times\)  ~ 0,001
\item   3 025  ~ \(\times\)  ~ 0,01
\item   61,82  ~ \(\times\)  ~ 0,001
\item   12,85  ~ \(\times\)  ~ 0,1
\item   225,7  ~ \(\times\)  ~ 0,001
\item   1,953  ~ \(\times\)  ~ 0,1
\item   16,1  ~ \(\times\)  ~ 0,001
\item   17,11  ~ \(\times\)  ~ 0,01
\item   75,1  ~ \(\times\)  ~ 0,01
\item   3 864  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   8 020  ~ \(\times\)  ~ ... ~ = ~  802
\item   7 951  ~ \(\times\)  ~ ... ~ = ~  795,1
\item   776,8  ~ \(\times\)  ~ ... ~ = ~  77,68
\item   9,21  ~ \(\times\)  ~ ... ~ = ~  0,092 1
\item   16,55  ~ \(\times\)  ~ ... ~ = ~  1,655
\item   16,65  ~ \(\times\)  ~ ... ~ = ~  0,166 5
\item   4 574  ~ \(\times\)  ~ ... ~ = ~  45,74
\item   2,389  ~ \(\times\)  ~ ... ~ = ~  0,002 389
\item   2,978  ~ \(\times\)  ~ ... ~ = ~  0,297 8
\item   80,94  ~ \(\times\)  ~ ... ~ = ~  8,094
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   516,15 ~m~ = ...~hm
\item   2 758,1 ~L~ = ...~cL
\item   4 592,2 ~kg~ = ...~dag
\item   496,73 ~g~ = ...~hg
\item   6 455 ~mL~ = ...~hL
\item   7 207,1 ~hL~ = ...~cL
\item   616,72 ~cm~ = ...~m
\item   342,21 ~g~ = ...~mg
\item   650,32 ~dL~ = ...~cL
\item   2 178,6 ~mg~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{3100}{100}\) = \(\dfrac{310}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{84}{10}\) = \(\dfrac{840}{100}\)
\item   \(\dfrac{22}{100}\) = \(\dfrac{220}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,8}
\item   430  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 43 000}
\item   31,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 319}
\item   72,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 727}
\item   353  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 35 300}
\item   0,03  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3}
\item   0,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5}
\item   0,831  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 831}
\item   4,71  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 710}
\item   562  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 562 000}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   796,4 ~ : ~ 100 ~ = ~{\color{red} 7,964}
\item   7 610 ~ : ~ 10 ~ = ~{\color{red} 761}
\item   22,15 ~ : ~ 10 ~ = ~{\color{red} 2,215}
\item   1 298 ~ : ~ 1 000 ~ = ~{\color{red} 1,298}
\item   63,45 ~ : ~ 10 ~ = ~{\color{red} 6,345}
\item   1 528 ~ : ~ 100 ~ = ~{\color{red} 15,28}
\item   3 345 ~ : ~ 10 ~ = ~{\color{red} 334,5}
\item   9 649 ~ : ~ 10 ~ = ~{\color{red} 964,9}
\item   555,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,555 1}
\item   94,97 ~ : ~ 10 ~ = ~{\color{red} 9,497}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   79 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 900
\item   0,52 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~520
\item   4,75 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~475
\item   58,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~58 900
\item   0,085 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,5
\item   9,68 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~96,8
\item   0,65 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,5
\item   73,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~735
\item   0,054 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,4
\item   0,009 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   5 436 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,436
}\item   3 025 ~ \(\times\)  0,01 ~ = ~{\color{red} 30,25
}\item   61,82 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,061 82
}\item   12,85 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,285
}\item   225,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,225 7
}\item   1,953 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,195 3
}\item   16,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,016 1
}\item   17,11 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,171 1
}\item   75,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,751
}\item   3 864 ~ \(\times\)  0,1 ~ = ~{\color{red} 386,4
}\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   8 020 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 802
\item   7 951 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 795,1
\item   776,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,68
\item   9,21 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,092 1
\item   16,55 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,655
\item   16,65 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,166 5
\item   4 574 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 45,74
\item   2,389 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 389
\item   2,978 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,297 8
\item   80,94 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,094
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   516,15 ~m~ = {\color{red}  5,161 5 }~hm
\item   2 758,1 ~L~ = {\color{red}  275 810 }~cL
\item   4 592,2 ~kg~ = {\color{red}  459 220 }~dag
\item   496,73 ~g~ = {\color{red}  4,967 3 }~hg
\item   6 455 ~mL~ = {\color{red}  0,064 55 }~hL
\item   7 207,1 ~hL~ = {\color{red}  72 071 000 }~cL
\item   616,72 ~cm~ = {\color{red}  6,167 2 }~m
\item   342,21 ~g~ = {\color{red}  342 210 }~mg
\item   650,32 ~dL~ = {\color{red}  6 503,2 }~cL
\item   2 178,6 ~mg~ = {\color{red}  0,217 86 }~dag
\end{itemize}
\end{multicols}
\end{document}
